Local atomic structures around Mn in $(\mathrm{Zn},\mathrm{Sn},\mathrm{Mn}){\mathrm{As}}_{2}$ thin films grown on InP (001) substrates were studied using x-ray fluorescence holography. The reconstructed three-dimensional atomic images showed that the addition of Mn resulted in further distortions of the As sublattice from the pure sphalerite ${\mathrm{ZnSnAs}}_{2}$. The first-principles calculations showed that the further distortion could be attributed to the shortening of the Mn-As bond length induced by the p-d exchange mechanism, which mediates the ferromagnetism in this material. In addition, we found that the positional fluctuation of the cations was maximized at the second nearest neighbor cation shell from detailed analysis of the atomic images. This anomaly in the fluctuation could be explained by the calculated forces acting on the cations.